Conditional Unbalanced Optimal Transport Maps: An Outlier-Robust Framework for Conditional Generative Modeling

• URL: http://arxiv.org/abs/2603.06972v2
• Date: Thu, 12 Mar 2026 15:34:07 GMT
• Title: Conditional Unbalanced Optimal Transport Maps: An Outlier-Robust Framework for Conditional Generative Modeling
• Abstract summary: Conditional Unbalanced Optimal Transport (CUOT) problem relaxes conditional distribution-matching constraints through Csiszr divergence penalties.<n>We propose Conditional Unbalanced Optimal Transport Maps (CUOTM), an outlier-robust conditional generative model built upon a triangular $c$-transform parameterization.<n>Our experiments on 2D synthetic and image-scale datasets demonstrate that CUOTM achieves superior outlier robustness and competitive distribution-matching performance.
• Score: 9.488297561764211
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conditional Optimal Transport (COT) problem aims to find a transport map between conditional source and target distributions while minimizing the transport cost. Recently, these transport maps have been utilized in conditional generative modeling tasks to establish efficient mappings between the distributions. However, classical COT inherits a fundamental limitation of optimal transport, i.e., sensitivity to outliers, which arises from the hard distribution matching constraints. This limitation becomes more pronounced in a conditional setting, where each conditional distribution is estimated from a limited subset of data. To address this, we introduce the Conditional Unbalanced Optimal Transport (CUOT) framework, which relaxes conditional distribution-matching constraints through Csiszár divergence penalties while strictly preserving the conditioning marginals. We establish a rigorous formulation of the CUOT problem and derive its dual and semi-dual formulations. Based on the semi-dual form, we propose Conditional Unbalanced Optimal Transport Maps (CUOTM), an outlier-robust conditional generative model built upon a triangular $c$-transform parameterization. We theoretically justify the validity of this parameterization by proving that the optimal triangular map satisfies the $c$-transform relationships. Our experiments on 2D synthetic and image-scale datasets demonstrate that CUOTM achieves superior outlier robustness and competitive distribution-matching performance compared to existing COT-based baselines, while maintaining high sampling efficiency.

Related papers

• Coupled Optimal Transport with Landmark Constraints [64.98367856457412]
  An optimal transport (OT) model seeks a map or plan between distributions by minimizing a prescribed transport cost or distortion.<n>This paper proposes a novel coupled OT framework that leverages a small number of annotated landmarks to guide the recovery of an underlying deformation.<n>The proposed framework provides a principled connection between landmark-based registration and transport-based distribution matching.
  arXiv  Detail & Related papers  (2026-08-20T08:28:13Z)
• Convex Distance Operator Transport: A Convex and Geometry-Preserving Formulation [9.94046521985351]
  We introduce Convex Distance Transport Operator (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains.<n>CDOT employs an operator-based regularization that aligns aggregated distance structures by introducing distance and conditional expectation operators.
  arXiv  Detail & Related papers  (2026-06-01T10:38:09Z)
• Variational Entropic Optimal Transport [67.76725267984578]
  We propose Variational Entropic Optimal Transport (VarEOT) for domain translation problems.<n>VarEOT is based on an exact variational reformulation of the log-partition $log mathbbE[exp(cdot)$ as a tractable generalization over an auxiliary positive normalizer.<n> Experiments on synthetic data and unpaired image-to-image translation demonstrate competitive or improved translation quality.
  arXiv  Detail & Related papers  (2026-02-02T15:48:44Z)
• Pairwise Optimal Transports for Training All-to-All Flow-Based Condition Transfer Model [15.078804369762993]
  We propose a flow-based method for learning all-to-all transfer maps among conditional distributions.<n>We introduce a novel cost function that enables simultaneous learning of optimal transports for all pairs of conditional distributions.
  arXiv  Detail & Related papers  (2025-04-04T05:32:54Z)
• The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation [56.33404393159126]
  We propose a conditional optimal transport C2OT that adds a conditional weighting term in the cost matrix when computing the optimal transport assignment.<n> Experiments demonstrate that this simple fix works with both discrete and continuous conditions in 8gaussians-to-moons, CIFAR-10, ImageNet-32x32, and ImageNet-256x256.
  arXiv  Detail & Related papers  (2025-03-13T17:59:56Z)
• Optimal Transport-Guided Conditional Score-Based Diffusion Models [63.14903268958398]
  Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. To tackle the applications with partially paired or even unpaired dataset, we propose a novel Optimal Transport-guided Conditional Score-based diffusion model (OTCS) in this paper.
  arXiv  Detail & Related papers  (2023-11-02T13:28:44Z)
• A generative flow for conditional sampling via optimal transport [1.0486135378491266]
  This work proposes a non-parametric generative model that iteratively maps reference samples to the target. The model uses block-triangular transport maps, whose components are shown to characterize conditionals of the target distribution. These maps arise from solving an optimal transport problem with a weighted $L2$ cost function, thereby extending the data-driven approach in [Trigila and Tabak, 2016] for conditional sampling.
  arXiv  Detail & Related papers  (2023-07-09T05:36:26Z)
• Consistent Optimal Transport with Empirical Conditional Measures [0.6562256987706128]
  We consider the problem of Optimal Transportation (OT) between two joint distributions when conditioned on a common variable. We use kernelized-least-squares terms computed over the joint samples, which implicitly match the transport plan's conditional objective. Our methodology improves upon state-of-the-art methods when employed in applications like prompt learning for few-shot classification and conditional-generation in the context of predicting cell responses to treatment.
  arXiv  Detail & Related papers  (2023-05-25T10:01:57Z)
• Comparing Probability Distributions with Conditional Transport [63.11403041984197]
  We propose conditional transport (CT) as a new divergence and approximate it with the amortized CT (ACT) cost. ACT amortizes the computation of its conditional transport plans and comes with unbiased sample gradients that are straightforward to compute. On a wide variety of benchmark datasets generative modeling, substituting the default statistical distance of an existing generative adversarial network with ACT is shown to consistently improve the performance.
  arXiv  Detail & Related papers  (2020-12-28T05:14:22Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.